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In this paper we investigate the strong lensing statistics in galaxyclusters. We extract dark matter haloes from the Millennium-XXL simulation,compute their Einstein radius distribution, and find a very good agreement withMonte Carlo predictions produced with the MOKA code. The distribution of theEinstein radii is well described by a log-normal distribution, with aconsiderable fraction of the largest systems boosted by different projectioneffects. We discuss the importance of substructures and triaxiality in shapingthe size of the critical lines for cluster size haloes. We then model andinterpret the different deviations, accounting for the presence of a BrightCentral Galaxy (BCG) and two different stellar mass density profiles. Wepresent scaling relations between weak lensing quantities and the size of theEinstein radii. Finally we discuss how sensible is the distribution of theEinstein radii on the cosmological parameters {\Omega}_M-{\sigma}_8 findingthat cosmologies with higher {\Omega}_M and {\sigma}_8 possess a large sampleof strong lensing clusters. The Einstein radius distribution may helpdistinguish Planck13 and WMAP7 cosmology at 3{\sigma}.

Characterising Strong Lensing Galaxy Clusters using the Millennium-XXL and MOKA simulations